Part Three Develop a Theory

One theory about why the temperature changes throughout the seasons is that because of the tilt of the earth’s axis the angle of the sun’s rays hitting the earth’s surface changes throughout the year. In the summer, the northern hemisphere is
tilted toward the sun, thus getting more direct rays, and in the winter the northern hemisphere it tilted away from the sun thus getting less direct rays. Of course the southern hemisphere is just the opposite.

summer winter

To help you understand this better try this simple experiment. Shine a flashlight straight down on a piece of paper do that it makes a circle on the paper. Now tilt the flashlight so that the light hits the paper at an angle but at the same distance away.
What kind of shape does the light make on the paper now?__________________
How does the area of this shape compare to the area of the circle?____________

How can we get some data on this phenomenon? Go to your computer and open up
Geometer's Sketchpad. Under the file folder programs, find rays and open it up.

This little exercise will let you measure the change in the diameter of the circle or ellipse with changes in the angle of the light. To run the program just place the arrow icon on the point D and drag it along the arc. Notice that as the beam of light moves back and forth the angle it makes with the paper changes and the width of the spot changes too.